Embodiments of the present invention generally relate to quantitative differential interference contrast (DIC) devices with wavefront sensors. More specifically, certain embodiments relate to quantitative DIC devices with wavefront sensors used in applications such as microscopy or photography, and that are adapted to compute depth sectioning of specimens and other objects.
DIC microscopes render excellent contrast for optically transparent biological samples without the need of introducing exogenous contrast agents into the samples. Due to the noninvasive nature, DIC microscopes are widely used in biology laboratories.
Conventional DIC microscopes and other conventional DIC devices typically operate by first creating two identical illumination light fields exploiting polarization selection. FIG. 1 is a schematic drawing of a conventional DIC device 10 that operates by interfering slightly displaced duplicate image light fields of polarized light. The conventional DIC device 10 includes an illumination source 20 providing polarized light to an object 30. As illustrated, the light fields are transmitted through the object 30 and are laterally displaced with respect to each other along the x-direction. A net phase lag (typically π/2) is then introduced on one of the transmitted image light fields. The two light fields are allowed to interfere with each other at the image plane 40. More simply, the process is equivalent to duplicating the transmitted image light field, laterally displacing a copy slightly and detecting the interference of the two light fields at image plane 40.
Mathematically, this implies that the observed DIC intensity image 42 from the conventional DIC device 10 with a magnification factor of M is given by Eq. (1):
                                                                                          I                  DIC                                ⁡                                  (                                      x                    ,                    y                                    )                                            =                            ⁢                                                                                                            ψ                      DIC                                        ⁡                                          (                                              x                        ,                        y                                            )                                                                                        2                                                                                        =                            ⁢                                                B                  ⁡                                      (                                          x                      ,                      y                                        )                                                  +                                                      C                    ⁡                                          (                                              x                        ,                        y                                            )                                                        *                                      sin                    ⁡                                          (                                                                                                                                                                  arg                                ⁡                                                                  (                                                                      ψ                                    ⁡                                                                          (                                                                                                                        x                                          -                                                                                      Δ                                            /                                            2                                                                                                                          ,                                        y                                                                            )                                                                                                        )                                                                                            -                                                                                                                                                                                          arg                              ⁡                                                              (                                                                  ψ                                  ⁡                                                                      (                                                                                                                  x                                        +                                                                                  Δ                                          /                                          2                                                                                                                    ,                                      y                                                                        )                                                                                                  )                                                                                                                                                        )                                                                                                                                              ≈                            ⁢                                                B                  ⁡                                      (                                          x                      ,                      y                                        )                                                  +                                                      C                    ⁡                                          (                                              x                        ,                        y                                            )                                                        *                                      (                                                                                                                                                      arg                              ⁢                                                              (                                                                  ψ                                  ⁡                                                                      (                                                                                                                  x                                        -                                                                                  Δ                                          /                                          2                                                                                                                    ,                                      y                                                                        )                                                                                                  )                                                                                      -                                                                                                                                                                            arg                            ⁢                                                          (                                                              ψ                                ⁡                                                                  (                                                                                                            x                                      +                                                                              Δ                                        /                                        2                                                                                                              ,                                    y                                                                    )                                                                                            )                                                                                                                                            )                                                                                                          (        1        )            where B(x, y)=|(ψ(x−Δ/2,y))|2+|(ψ(x+Δ/2,y))|2,C(x, y)=2|(ψ(x−Δ/2,y))∥(ψ(x+Δ/2,y))|, and ψ(x, y) is the image wavefront as relayed by the microscope for each light field, ψDIC(x, y) is the DIC image wavefront, and Δ=Ma is the relative displacement of the images associated with the light fields. The last expression in Eq. (1) is valid only in situations where the phase difference is small.
However, conventional DIC devices have several limitations. One major limitation is that conventional DIC devices translate phase variations into amplitude (intensity) variations. As shown in Eq. (1), the DIC intensity image, IDIC(x,y) is a sine function of the differential phase so that the phase information cannot be interpreted directly from the intensity of the DIC image. Also, the B(x,y) and C(x,y) terms both contain amplitude information so that the DIC image contains entangled amplitude and phase information. Therefore, phase variations cannot be easily disentangled from amplitude (intensity) variations that arise from absorption and/or scattering by an object. In other words, conventional DIC devices do not distinguish between the effects of absorption and phase variation. As a consequence of this entanglement of amplitude and phase information and nonlinear phase gradient response, conventional DIC devices are inherently qualitative and do not provide quantitative phase measurements
Another limitation of conventional DIC devices is that they use polarized light and depend on the polarization in their phase-imaging strategies. Since polarized light must be used, conventional DIC devices generate images of birefringent objects (e.g., potato starch storage granules) that typically suffer from significant artifacts.